Question 601435
How do I find the answer to the following math word problem? "Mila took a trip and drove the first 20 miles at a speed of 50 mph. If she wants her average speed for the entire trip to be 40 mph, how fast should she drive for the last 70 miles of her trip?"
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For the first part of the trip, the travel time = 20 mi/50 mi/h = 2/5 hr
The average speed for the entire trip is the total distance divided by the total time:
v = (d1+d2)/(t1+t2) = 40 mph = (20+70)/(2/5+t2)
Solve for t2:
90/(2/5 + t2) = 40
t2 = 9/4 - 2/5 = 37/20 hr
So the speed for the last 70 miles of the trip is 70 mi/(37/20 hr) = 37.838 mph
Check:
90/(2/5+37/20) = 90/2.25 = 40